Well, first of all, intuitively it's actually a proxy for offensive zone possession. In order to direct a shot attempt at your opponent's goal, you must have the puck in the offensive zone. For the same reason, goals or shots would also be a proxy for offensive zone possession, but they're significantly rarer than shot attempts. So corsi and fenwick are used essentially because of sample size. For every game, teams each take an average of 29 or so shots. However, they direct more than twice as many shot attempts at the net. So you have twice as many instances where you can say, "this team had the puck in the offensive zone".
Does it, practically speaking, correlate to offensive puck possession in the sense of "guy on the Canadiens had the puck on his stick in the offensive zone for X second"? All attempts to track this have suggested it's very close.
Because of the time and effort it takes to hold two stopwatches in hand, it's not done very much. There may be other instances of people doing this, but once you've done it for a bit and see "yeah, it's basically the same", I would imagine your desire to keep going wanes. There's never been anyone I know of who's attempted this and found a significant difference between corsi and actual time of possession. We'll know for certain once sportVU comes in, though. It would be very surprising to see anything significantly different from that graph.